A Fluid Introduction to Brownian Motion and Stochastic Integration

DOI10.1007/978-1-4614-4909-6_10zbMath1282.60082OpenAlexW128117562MaRDI QIDQ2841728

Vaidyanathan Ramaswami

Publication date: 29 July 2013

Published in: Matrix-Analytic Methods in Stochastic Models (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4614-4909-6_10

zbMATH Keywords

Brownian motionstochastic integrationfluid flow models

Mathematics Subject Classification ID

Brownian motion (60J65) Stochastic integrals (60H05)

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Total shift during the first passages of Markov-modulated Brownian motion with bilateral ph-type jumps: Formulas driven by the minimal solution matrix of a Riccati equation ⋮ Rate of strong convergence to Markov-modulated Brownian motion ⋮ Markov-modulated Brownian motions perturbed by catastrophes ⋮ Strong convergence to two-dimensional alternating Brownian motion processes ⋮ An explicit solution to the Skorokhod embedding problem for double exponential increments ⋮ A quadratically convergent algorithm for first passage time distributions in the Markov-modulated Brownian motion ⋮ Markov-modulated Brownian motion with temporary change of regime at level zero ⋮ Time-dependent and stationary analyses of two-sided reflected Markov-modulated Brownian motion with bilateral ph-type jumps ⋮ The morphing of fluid queues into Markov-modulated Brownian motion ⋮ Alternative fluid approximation approach for the steady-state distribution of the two-sided reflected Markov modulated Brownian motion and its computation

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